Method of designing minute flow rate controller with entrance throttle groove

ABSTRACT

A method of designing a minute flow rate controller that is capable of accurately controlling the minute flow rate of a fluid and realizing desired valve characteristics without inducing any unsteadiness of fluid flow and has a simple configuration with respect to a throttle groove for controlling the fluid flow rate. With respect to a minute flow rate controller comprising inflow passage ( 12 ) for introducing a fluid, valve member ( 2 ) furnished with main throttle groove ( 6 ) for causing the introduced fluid to flow from a starting end toward a finishing end thereof, fluid outflow port ( 20 ) opened with an optional cross section by a flow rate regulating member and outflow passage ( 14 ) for leading out the fluid flowing out from the fluid outflow port ( 20 ), there is provided a method of designing the minute flow rate controller with entrance throttle groove, comprising providing entrance throttle groove ( 8 ) communicably preceding the starting end position of the main throttle groove ( 6 ), and, on the basis of a relational expression derived from the momentum equation of the fluid flowing through the entrance throttle groove ( 8 ) and the main throttle groove ( 6 ), determining the size of the entrance throttle groove ( 8 ) so as to exhibit a desired flow resistance.

FIELD OF THE INVENTION

The present invention relates to a flow rate controller that controlsflow of liquid or gas. More specifically, this relates to a method fordesigning a minute flow rate controller that controls minute flow offluid (liquid or gas) in an extremely minute sized (such as microsized)flow path, environment for fluid movement, or reactor.

BACKGROUND ART

Recently, microminiaturization and integration of chemical reactionsystems have been attracting attention as new technical subjects insynthetic chemistry, analytical chemistry, semiconductor industry, andbiotechnology industry. It is thought that such microminiaturization andintegration will play an important role in improving precision andpromoting efficiency in the control of chemical reaction in systems forimmunoassay, environmental analysis, cell biochemistry experiment,chemical gas-phase growth, and synthetic chemistry experiment. In suchtechnological trend, new research and development is about to bepromoted, whose subject is chemical reaction whose reaction capacity isa minuscule space from nanoliter to microliter, a so-calledmicroreactor; and whose objective is improvement of reaction yield,shortening of reaction time, and decrease of burden to the environment.For the liquid or gas to be supplied to such a minute space, minute andprecise flow control that is nonexistent in the existing technology isconsidered to be indispensable.

Conventionally, as the valve type used for minute flow adjustment offluid, the needle valve type is usually used. As for the needle valve,since the flow rate increases suddenly after opening of the valve, it isdifficult to employ it as a means to adjust the flow rate (for example,the maximum flow of 10 mL/min-1 mL/min for liquid, or a minute flow rateof 1-0.01 sccm for gas) supplied to said minute space. Therefore, thedevelopment of a new minute flow rate control technology suitable forsuch purpose has become necessary.

As for prior arts for minute flow rate control valves whose mechanism isdifferent from the needle valve type, Japanese Patent Laid-Open No.2001-187977 (patent document 1) and Japanese Patent Laid-Open No.2003-278934 (patent document 2) have been made public. Both of theseprior arts are characterized by the configuration in which the throttlegroove that controls the fluid flow rate is arranged in an arc-shape.

[Patent Document 1] Japanese Patent Laid-Open No. 2001-187977

[Patent Document 2] Japanese Patent Laid-Open No. 2003-278934

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

FIG. 21 is an exploded perspective assembly view of the conventionalflow control valve taught in the patent document 1. The main body of thevalve, centralized on the central axis Z, is composed of the valve seat110 and the valve member 103, and the metal valve 102 which forms thethrottle groove 104 is located between the valve seat 110 and the valvemember 103. The exit flow passage 114 is installed on the valve seat110, and the groove portion 103 a for the entrance flow passage isformed on the valve member 103. The fluid is led through the grooveportion for the entrance flow passage 103 a that is formed on the valvemember 110, led through the throttle groove 104 that is formed on themetal valve 102, its flow rate controlled by the angle of rotationaround the axis Z of the exit flow passage 114 located on the valve seat110, and is led from the L-shaped exit flow passage 114 that is formedon the valve seat to the valve exit 114 a. The rotation of this valveseat 110 is performed with a stepping motor placed at the upper part.

FIG. 22 is a plan view of the throttle groove 104 formed on the metalvalve 102 in FIG. 21. The throttle groove 104 is formed around theZ-axis on the arc with radius r; its depth h remains constant, and itswidth W maximizes at the front end region, and is configured so that itgradually narrows toward the back end region. In the starting endposition of the throttle groove 104, the through hole 113 that connectsto the groove portion 103 a for the entrance flow passage (FIG. 21) isformed. The flow rate of the fluid introduced through this hole 113 iscontrolled by the angle of rotation around the Z-axis of the L-shapedexit flow passage 114 formed on the valve seat 110.

Therefore, in order to adjust the fluid flow rate minutely, it becomesimportant that the valve seat 114 is rotated minutely. However, becausethe quantity of circumferential displacement by the rotation isproportional to the product of the circle radius and the rotation angle,the quantity of angle rotation becomes relatively small when the circleradius is large. Normally, not only with the needle valve but also withthe flow rate control valve, in order to control minutely the extremelysmall circumferential displacement immediately after opening of thevalve, it also becomes necessary to control minutely the angle ofrotation. However, when the circle radius is large, the adjustment ofthe rotation angle must be performed even more minutely, which meansthat the minute flow rate control becomes even more difficult. On theother hand, when the circle radius is small, it conversely becomesdifficult to engrave such arc-shaped throttle groove precisely.Therefore, in the arc-shaped throttle groove, the circle radius becomesnecessarily large, and a difficulty in minute angle control arises.

The length from the starting end position 104 a of the throttle groove104 to the finishing end position 104 b is defined as L₀; and the lengthof the throttle groove 104 from the aperture cross section 114 b whichis formed on the exit flow passage 114 a, to the finishing end 104 b ofthe throttle groove, is defined as L. The ratio between the length L ofthe aperture and its maximum length L₀ is defined as L*. L* varieswithin the limits of 0-1. When the valve moves straightly, it signifiesthe dimensionless length of the lift (also called relative travel).Henceforth, L* is termed dimensionless lift.

The present inventor has analyzed the relation between the extent ofvalve opening of a minute flow rate controller and the flow rate, orthat is to say, the requirement in changing the cross section area ofthe throttle groove along the flow passage in order to make the flowrate characteristic equal to a desired characteristic, and haveinvestigated the characteristics observed in the change in the axialdirection of the cross section area of the throttle groove with thechange in various design parameters such as the physical characteristicsof the fluid, the differential pressure between the front and the backof the valve, the height and the aspect ratio (the ratio between theheight and the width) whenever the configuration of the cross section isrectangular, and the length of the groove. By the way, the flow ratecharacteristic of the flow rate adjustment valve is called the valvecharacteristic; among this, there are the linear characteristic and theequal percentage characteristic, and usually it is designed so thateither characteristic is imparted. The basic attribute found in the flowrate characteristic of minute flow rate controller will be described forthe case in which the valve characteristic of the linear type isimparted. In FIG. 23, water of 20 degrees Celsius is used as thereference for the physical property values of the fluid; and itindicates the requirement in changing the cross section area of thethrottle groove in the flow direction, in order to equalize the valvecharacteristic of the required linear type, when the viscositycoefficient becomes 10 times to 20 times that of this water.

FIG. 23 is the correlation diagram for a minute flow rate controller ofthe conventional type, in which the dimensionless length L* referencedto the length of the throttle groove (corresponding to the dimensionlesslift when the length of the groove is taken with the purpose of makingL*=1 when the valve is fully opened) is made to be the abcissa, and theratio between the cross section area at a given position and theentrance cross section area of the groove (the dimensionless crosssection area A*) and the dimensionless flow rate Q* (volumetric flowrate ratio) based on the flow rate at the time of full opening of thevalve are made to be the ordinates. The configuration of the throttlegroove cross section is rectangular, its length L₀ is 10 mm and itsheight H₀ uniformly 0.5 mm, and the aspect ratio Ca of the groove is 1.5at the entrance of the throttle groove. In addition, the differentialpressure between the entrance and the exit of the valve is set to be0.001 MPa (flow rate of about 12 mL/min at the full opening position).Usually, for either the linear characteristic or the equal percentagecharacteristic, when the value of G* (mass flow rate ratio: same as Q*in the case of liquid) generated immediately after valve opening is setto G*₀, its reciprocal 1/G*₀ corresponds to the quantity of the abilityof said valve for controlling the flow rate, expressed in a multiple ofthe flow rate immediately after the valve opening; this is termedrangeability (henceforth denoted as R_(A)). FIG. 23 shows the case inwhich R_(A)=20. The cross section area of the throttle groove does notvary monotonically with respect to the dimensionless lift. As shown inFIG. 23, it may take the form of a curve taking its maximum betweenL*=0-1, and with an increase of viscosity, it becomes a curve having asteeper peak. As a general trend, the maximum of the dimensionless crosssection area A* increases along with the decrease in the depth of thegroove and the increase of the aspect ratio at the entrance of thegroove. These signify that the maximum of A* increases as the flow ratedecreases. Therefore, in the case of an extremely minute flow rate of 10mL/min or less, which is considered to be a problem in a microreactor,there is a tendency for the curve to take a prominent peak, even for afluid of relatively low viscosity. Such tendency not only makes theprocessing of the groove difficult, but also makes probable that aseparation of the flow accompanying an immediate expansion of the flowpassage cross section area is caused, and the flow characteristic ismade unstable. In addition, upon a change in the condition of usage, achange is caused in the flow rate in which the valve characteristicdeviates from the linear characteristic type. The tendencies describedabove may become apparent and turn into problems even for the case inwhich the valve characteristic is of the equal percentagecharacteristic.

On the other hand, the electrically operated flow rate control valvedescribed in Japanese Patent Laid-Open No. 2003-278934 (patent document2) is configured from an upper valve and a lower valve, and thehermeticity of the valve is increased by applying fluid pressure to thelower valve by opening and closing of the upper valve. However, becauseit is mechanically similar to the electrically operated flow ratecontrol valve described in the patent document 1, a separation of thefluid flow is caused, accompanying an immediate expansion of the flowpassage cross section area, and the previously mentioned problems suchas the destabilization of the flow characteristic are present. Thepresent inventor studied intensively to solve this problem, and as theresult, came up with the idea of imparting flow resistance upstream ofthe throttle groove; and based on the hydrodynamic theory, derived themethod of designing the structure of a throttle groove that causes thisflow resistance, and thus completed the present invention.

The objective of the present invention is to realize a desired valvecharacteristic without giving rise to a flow instability upon forming asuddenly expanded portion of the flow as seen in FIG. 23, in order tocontrol stably and accurately the minute flow rate of the fluid. Inother words, it is to provide a design method of a minute flow ratecontroller that can realize a desired valve characteristic, under thecondition in which the cross section area of main throttle groove isvaried monotonically along the flow direction, by placing an entrancethrottle groove that impart a flow resistance of appropriate quantity atthe entrance side of the main throttle groove.

Means to Solve the Problem

The present invention was achieved in order to solve the problem. Thefirst form of the present invention is a method of designing a minuteflow rate controller equipped with an entrance throttle groove, saidminute flow rate controller comprising an inflow passage for introducinga fluid, a valve member on which a main throttle groove is formed, forflowing the fluid introduced from said inflow passage from a startingend to a finishing end, a flow rate regulating component thathermetically seals said main throttle groove up to a desired position, afluid outflow port that opens by said flow rate regulating component ata given cross section of said main throttle groove, and an outflowpassage that lead out the fluid that flows out of said fluid outflowport, wherein an entrance throttle groove that precedes connectively isestablished at the starting end cross section of said main throttlegroove, and the dimension of the entrance throttle groove is determinedso as to exhibit a desired flow resistance, based on a relationalequation derived from a momentum equation of the fluid that flowsthrough said entrance throttle groove and main throttle groove.

The second form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said first form, wherein the dimension of said entrancethrottle groove is determined so that when the cross section area ofsaid main throttle groove monotonically decreases from the starting endto the finishing end, the flow rate of the fluid that flows out fromsaid fluid outflow port monotonically decreases, as the position of saidfluid outflow port moves from the starting end to the finishing end.

The third form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to either of said first or second form, wherein the momentumequation of said fluid is expressed as uρ(du/dz)+(λ/D_(H))(½)u²ρ+dP/dz=0(here, u is the flow velocity, ρ is the density, z is the flow directioncoordinate of fluid, λ is the friction coefficient, D_(H) is theequivalent diameter of throttle groove cross section area, and P is thepressure)

The fourth form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said third form, wherein said momentum equation is computedbased upon u=G/(ρA) and λ=64 μA/(GD_(H)) (here, G is the mass flow rate,ρis the fluid density, A is the cross section area of the fluid outflowport, and μ is the viscosity coefficient of the fluid).

The fifth form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said fourth form, wherein the critical length of theentrance throttle groove L_(EC) is given as L_(EC)=L₀/(dG*/dL*)_(L*=1),whenever the finishing end position of said main throttle groove is setat L=0, the position of the fluid outflow port is set at L=L, thestarting end position is set at L=L₀, the flow rate when the fluidoutflow port is located at L=L₀ is set at G_(M), the flow rate when thefluid output port is located at L=L is set at G, and the value of(dG*/dL*) at L*=L/L₀, G*=G/G_(M), and the value of (dG*/dL*) at L*=1 isset to (dG*/dL*)_(L*=1).

The sixth form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said fifth form, wherein the critical length L_(EC)corresponding to the linear type, in which the valve characteristic maybe expressed as G*=L*, is given as L_(EC)=L₀, whenever said fluid is anincompressible fluid, and the forms of given cross sections of the mainthrottle groove are similar figures.

The seventh form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said fourth form, wherein said critical length L_(EC) isgiven by L_(EC)=L₀/(dG*/dL*), whenever the finishing end position ofsaid main throttle groove is at L=0, the position of the fluid outflowport is at L=L, the starting end position is at L=L₀, the flow rate whenthe fluid outflow port is at L=L₀ is G_(M), the flow rate when the fluidoutflow is at L=L is G, the forms of given cross sections of said mainthrottle groove are non-similar figures, and the valve characteristic isof the linear type.

The eighth form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said fifth or seventh form, wherein said critical lengthL_(EC) is given by L_(EC)=L₀/(1−1/R_(A)), whenever the valvecharacteristic is of the linear type, and may be expressed asG*=G₀*+(1−G₀*)L* (here, G₀* is the value of G* at L*=0), and may beexpressed as G₀*=1/R_(A)(1≦R_(A)≦∞).

The ninth form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said fifth or seventh form, wherein said critical lengthL_(EC) is given as L_(EC)=L₀/ln(R_(A)), whenever the valvecharacteristic is of the equal percentage type that may be expressed asG*=G₀*^((1−L)*⁾ (here, G₀* is the value of G* when L*=0), and whereG₀*=1/R_(A)(1≦R_(A)≦∞).

The tenth form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to any of said first to fourth forms, wherein it is equippedwith an entrance throttle groove in which the cross section area of saidentrance throttle groove increases monotonically toward the starting endposition of said main throttle groove.

The eleventh form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said tenth form, wherein the cross section area A_(E)(z) ofsaid entrance throttle groove increases linearly along the flowdirection coordinate z, and said cross section area A_(E)(z) is given asA_(E)(z)=A_(EQ)+{(A_(E0)−A_(EQ))/L_(EQ)}·z (here, A_(EQ) is the startingend cross section area of the entrance throttle groove, A_(E0) is thefinishing end cross section area of the entrance throttle groove nearestto the starting end position of said main throttle groove, L_(EQ) is thelength of the entrance throttle groove, and z is the flow directioncoordinate of the fluid).

The twelfth form of the present invention is the method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to said eleventh form, wherein the finishing end position ofsaid main throttle groove is L=0, the starting end position is L=L₀, theflow rate when the fluid overflow port is at L=0 is G₀, the flow ratewhen the fluid overflow port is at L=L₀ is G_(M), G₀*=G₀/G_(M),R_(A)=1/G₀*, and the subsequent lengthL_(EQ)=(A_(EQ)/A_(E0)){L₀/(1−G₀*)}=(A_(EQ)/A_(E0)){L₀/(1−1/R_(A))} ofthe entrance throttle groove, obtained by assuming that the frictionalpressure drop inside said entrance throttle groove takes an equivalentquantity to the frictional pressure drop exhibited by an entrancethrottle groove with a constant cross section area whose critical lengthL_(EC), is taken.

Effect of the Invention

According to the first form of the present invention, because thedimension of the entrance groove, which is connectedly formed precedingthe starting end position of the main throttle groove in the minute flowrate controller, is determined according to the relational equationderived from the momentum equation of the fluid that flows through thethrottle groove, by forming the entrance throttle groove designed by thedesign method of the present invention, the dimension of the mainthrottle groove that has a simple structure, and realizes the desiredvalve characteristic, can be determined. In other words, because thedimension of the entrance throttle groove that exhibits a flowresistance matching the desired valve characteristic is determined basedon said relational equation, there is no need to vary the cross sectionarea of the main throttle groove precipitously or delicately in order torealize the desired valve characteristic; and the dimension of the crosssection area, varying monotonically along the axis, of the main throttlegroove can be determined. In addition, the relational equation fordetermining the dimension of the entrance throttle groove can be derivedfrom the momentum equation, under the condition that the desired valvecharacteristic is imparted. In addition, by forming the entrancethrottle groove designed by the design method of the present invention,a highly accurate control of the minute flow rate can be easilyperformed through the minute flow rate controller equipped with the mainthrottle groove with a simple structure. Furthermore, by said mainthrottle groove having a simple structure, a highly precise minute flowrate controller can be produced easily, and the production cost of theminute flow rate controller can be reduced.

According to the second form of the present invention, the flow rate canbe adjusted with high accuracy through the minute flow rate controlleron which the main throttle groove whose cross section area decreasingmonotonically from the starting end to the finishing end. As describedpreviously, in the conventional minute flow rate controller, it wasnecessary to narrow the vicinity of the starting end of the mainthrottle groove in order to realize a monotonical decrease by moving theflow rate regulating component. However, by forming connectively theentrance throttle groove of the present invention, it is possible torealize the desired flow rate characteristic through the main throttlegroove whose cross section area varies monotonically. Said main throttlegroove, whose cross section area decreases monotonically, is easilyformed on said valve member, and can process the form of the designedmain throttle groove with high precision. Therefore, a highly preciseminute flow rate controller can be offered, and at the same time, theyield in production can be improved markedly.

According to the third form of of the present invention, by applying

uρ(du/dz)+(λ/D _(H))(½)u ² ρ+dP/dz=0   (1)

(here, u is the flow velocity, ρ is the density, z is the flow directioncoordinate, λ is the friction coefficient, D_(H) is the equivalentdiameter of the throttle groove cross section area, and P is thepressure) as said fluid momentum equation, said relational equation canbe derived. Here, for a throttle groove having an arbitrarycross-section form, the equivalent diameter D_(H) defined as D_(H)=4A/Uis used.

According to the fourth form of the present invention, because the flowvelocity u is expressed as

u=G/(ρA)   (2)

the relational equation may include the cross section area A of thethrottle groove and the mass flow rate G as variables or parameters, andthe relation between the desired valve characteristic and the dimensionof the entrance throttle groove can be formulated clearly. Furthermore,by assuming the flow in the throttle groove to be a laminar flow, saidfriction coefficient λ depends upon only the Reynolds number Re of thefluid, where

λ=64/Re   (3).

Here, the Reynolds number is defined in the next equation.

Re=D _(H) u/(μ/ρ)   (4)

Therefore, because it follows that

λ=64 μA/(GD _(H))   (5)

said friction coefficient λ may easily be derived.

According to the fifth form of the present invention, when the finishingend position of said main throttle groove is at L=0, the position of thefluid outflow port is at L=L, the starting end position is at L=L₀, thecross section area of the main throttle groove when L=L is A, the flowrate when the fluid outflow port is at L=L₀ is G_(M), the flow rate whenthe fluid outflow port is at L=L is G, L*=L/L₀, G*=G/G_(M), and thevalue of (dG*/dL*) at L*=1 is (dG*/dL*)_(L*=1), the critical lengthL_(EC) of the entrance throttle groove is given by

L _(EC) =L ₀/(dG*/dL*)_(L*=1)   (6),

and one may determine the dimensionless cross section area A* (=A/A_(E))of the main throttle groove by solving for said momentum equation underthe desired valve characteristic. A* derived thus becomes G*=A* at thevicinity of L*=1. Furthermore, A* has a characteristic that it variesmonotonically in the axial direction. Such design technique can beapplied whether or not the fluid is compressible, whether or not thecross section forms of the throttle groove are similar in the axialdirection, or whether or not the valve characteristic is of the lineartype or the equal percentage type.

According to the sixth form of the present invention, when said fluid isan incompressible fluid, and the forms of arbitrary cross sections ofthe main throttle groove are similar to one another, the critical lengthL_(EC) for the linear type whose valve characteristic is expressed asG*=L* is given as

L_(EC)=L₀   (7)

and by setting A*=L*, valve characteristic such that it becomes G*=L*can be realized. When the momentum equation is applied to an entrancethrottle groove whose critical length L_(EC) is set by L_(EC)=L₀, andconnecting with this, a flow passage consisting of a main throttlegroove, G*=A*=L* is derived as the relation between the valvecharacteristic and the dimensionless cross section area A* of the mainthrottle groove. Therefore, if the entrance throttle groove is set toL_(EC)=L₀, one can impart a simple valve characteristic onto the minuteflow rate controller, in which the flow rate G becomes a simple multipleof the position L of the fluid outflow port, and control the minute flowrate can be performed easily and with high accuracy, by choosing thedimension the cross section of of the main throttle groove for thepurpose of achieving A*=L*.

According to the seventh form of the present invention, whenever thefinishing end position of said main throttle groove is at L=0, theposition of the fluid outflow port is at L=L, the starting end positionis at L=L₀, the flow rate when the fluid outflow port is at L=L₀ isG_(M), the flow rate when the fluid outflow port at L=L is G, the formsof arbitrary cross sections of said main throttle groove arenon-similar, L*=L/L₀, G*=G/G_(M), and the valve characteristic is of thelinear type, said critical length L_(EC) is given by

L _(EC) =L ₀/(dG*/dL*)   (8)

and by solving for the said momentum equation for the desired valvecharacteristic, the dimensionless cross section area A* of the mainthrottle groove that varies monotonically along the axial direction maybe determined.

According to the eighth form of the present invention, whenever thevalve characteristic is of the linear form that is expressed as

G*=G ₀*+(1−G ₀*)L*   (9)

said critical length L_(EC) is expressed as

L_(EC) =L ₀/(1−1/R _(A))   (10)

and therefore, when said length L₀ of the main throttle groove and therangeability R_(A) are given, the critical length of the entrancethrottle groove that imparts the valve characteristic of said lineartype is easily determined. The dimensionless flow rate G*₀ correspondsto the magnitude when the flow rate regulating ability of the valve isexpressed as a multiple of the flow rate immediately after the valveopening; the rangeability R_(A) is defined as the inverse 1/G*₀ of G*₀,and it is the quantity that characterizes the valve characteristic inthe vicinity of the full closing state (L*=0).

According to the ninth form of the present invention, whenever the valvecharacteristic is of the equal percentage type that is expressed by

G*=G ₀*^((1−L)*⁾   (11)

and G₀* is the value of G* at L*=0, and is expressed asG₀*=1/R_(A)(1≦R_(A)≦∞), because said critical length L_(EC) is given by

L _(EC) =L ₀/ln(R _(A))   (12)

the length of the entrance throttle groove that realizes the valvecharacteristic of the equal percentage type may be determined.

According to the tenth form of the present invention, whenever the crosssection area of the finishing end position of said entrance throttlegroove is equal, because the flow resistance due to the entrancethrottle groove may be increased by monotonically increasing the crosssection area of the entrance groove toward the starting position of saidmain throttle groove, or in other words, by decreasing monotonicallytoward the entrance of the entrance throttle groove, the length of saidentrance throttle groove can be shortened. Therefore, the minute flowrate controller can be made compact.

According to the eleventh form of the present invention, because thecross section area of said entrance throttle groove increases linearlyalong the flow direction coordinate z, and said cross section area isgiven by

A _(E)(z)=A _(EQ)+{(A _(E0) −A _(EQ))/L _(EQ) }·z   (13)

the pressure loss of the fluid at this entrance throttle groove may beeasily estimated, at the same time as the flow resistancy due to saidentrance throttle groove increases. In other words, the dimension of theentrance throttle groove that gives the desired valve characteristic canbe easily determined.

According to the twelfth form of the present invention, because thelength of said entrance throttle groove is given by

$\begin{matrix}\begin{matrix}{L_{EQ} = {\left( {A_{EQ}/A_{E\; 0}} \right)\left( {L_{0}/\left( {1 - G_{0}^{*}} \right)} \right)}} \\{= {\left( {A_{EQ}/A_{E\; 0}} \right)\left( {L_{0}/\left( {1\text{-}{1/R_{A}^{*}}} \right)} \right)}}\end{matrix} & (14)\end{matrix}$

the length of the entrance throttle groove which imparts the valvecharacteristic of the linear type to the minute flow rate controller canbe determined easily.

BRIEF DESCRIPTION OF DR_(A) WINGS

FIG. 1 is a schematic illustration of the minute flow rate controller ofthe present invention.

FIG. 2 is a schematic cross-sectional view of the minute flow ratecontroller of the present invention.

FIG. 3 is a schematic cross-sectional view in which the minute flow ratecontroller of the present invention is in the full opening state.

FIG. 4 is a schematic cross-sectional view in which the minute flow ratecontroller of the present invention is in the full closing state.

FIG. 5 is a schematic plan view of the minute flow rate controller.

FIG. 6 is a schematic diagram of the throttle groove of the presentinvention.

FIG. 7 is a process chart for the calculation of the momentum equationof the present invention.

FIG. 8 is a process chart for the derivation of the relational equationof the present invention.

FIG. 9 is a process chart for the derivation of the relational equationfor an incompressible fluid.

FIG. 10 is a schematic diagram of the throttle groove that has similarcross section forms.

FIG. 11 is a classification figure of the critical length in the casewhere the valve characteristic is of the linear type.

FIG. 12 is a correlation diagram of the cross section area A and theflow rate Q of the main throttle groove in a minute flow ratecontroller, to which the valve characteristic of the linear type isimparted.

FIG. 13 is a correlation diagram of the cross section area A and theflow rate Q of the main throttle groove in a minute flow rate controllerto which the valve characteristic of the linear type is imparted.

FIG. 14 is a schematic diagram of a throttle groove having non-similarcross sections.

FIG. 15 is a correlation diagram of the cross section area A and theflow rate Q for a minute flow rate controller in which the length of theentrance throttle groove of the present invention is set to thequasicritical length L_(EC).

FIG. 16 is a classification figure of the critical length when the valvecharacteristic is of the equal percentage (EQ) type.

FIG. 17 is a correlation diagram of the cross section area A and theflow rate Q of the main throttle groove in a minute flow rate controllerto which the valve characteristic of the equal percentage type isimparted.

FIG. 18 is a correlation diagram between the dimensionless cross sectionarea A* and the dimensionless flow rate Q* of the main throttle groovein a minute flow rate controller to which the valve characteristic ofthe equal percentage type is imparted.

FIG. 19 is a schematic diagram of the throttle groove having a shortenedentrance throttle groove.

FIG. 20 is a process chart for deriving the length of the shortenedentrance throttle groove of the present invention.

FIG. 21 is an exploded perspective assembly view of the conventionalflow control valve.

FIG. 22 is a plan view of the throttle groove 104 formed on the metalvalve in FIG. 21.

FIG. 23 is a correlation diagram that indicates the effect of thequantity of the fluid viscosity on the relation between the crosssection area of the throttle groove and the flow rate with respect tothe lift, in a conventional minute flow rate controller not equippedwith an entrance throttle groove.

DENOTATION OF REFERENCE NUMERALS

2 Valve member

4 Throttle groove

6 Main throttle groove

8 Entrance throttle groove

10 Flow rate regulating slider

10 a Sliding position

10 b Arrow

12 Inflow passage

14 Outflow passage

15 Inflow portion

16 Starting end cross section of entrance throttle groove

18 Starting end cross section of main throttle groove

19 Finishing end cross section of entrance throttle groove

20 Fluid outflow port

22 Outflow portion

24 Sliding range

24 a Full opening position

24 b Full closing position

26 Tube passage

26 a Minute column

102 Metal valve

103 Valve member

103 a Groove portion for entrance flow passage

104 Throttle groove

110 Valve seat

113 Through hole

114 Exit flow passage

114 a Valve exit

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 is a schematic illustration of the minute flow rate controller ofthe present invention. The basic structure of the minute flow ratecontroller consists of the valve member 2 on which throttle groove 4 isformed, and the flow rate regulating slider 10. The throttle groove 4 iscomposed of the main throttle groove 6 and the entrance throttle groove8, and the main throttle groove 6 and the entrance throttle groove 8functions as the flow passages, by said flow rate regulating slider 10sliding at the upper surface of the valve member. When said flow rateregulating slider 10 is at the sliding position 10 a on the top surfaceof the valve member 2, the fluid which flows from the inflow passage 12flows into the entrance throttle groove 8 through the inflow portion 15,flows out from the fluid outflow port 20 through said main throttlegroove 6, and flows into the outflow passage 14 through the outflowportion 22. The length of said main throttle groove 6 is varied, and thefluid flow rate is adjusted, by said flow rate regulating slider 10sliding in the direction of the arrow 10 b.

FIG. 2 is a schematic cross-sectional view of the minute flow ratecontroller of the present invention. The flow rate regulating slider 10slides on the top surface of the valve member 2, and can be moved freelywithin the sliding range 24 from the full opening position 24 a to thefull closing position 24 b. It is not shown in this figure, but on theslight-movement flow rate controller, an actuating means for moving theposition of the flow rate regulating slider 10 depending on the desiredflow rate is provided, and a slight-movement controlling meansconsisting of a stepping motor or a piezoelectric device can be used asthis actuating means.

FIG. 3 is a schematic cross-sectional view in which the minute flow ratecontroller of the present invention is in the full opening state. Whenan end of the flow rate regulating slider 10 is at the full openingposition 24 a within said sliding range 24, the cross section area 20 ofthe fluid outflow port 20 maximizes, and the maximum flow rate issupplied from the outflow portion 22 to the outflow passage 14.

FIG. 4 is a schematic cross-sectional view in which the minute flow ratecontroller of the present invention is in the full closing state. Whenthe end surface of the flow rate regulating slider 10 is at the fullclosing position 24 b within the sliding range 24, the outflow portionbecomes completely closed by said flow rate regulating slider, and theflow rate becomes 0.

FIG. 5 is a schematic plan view of the minute flow rate controller. Saidmomentum equation (1)

uρ(du/dz)+(λ/D _(H))(½)u ² ρ+dP/dz=0   (1)

(here, u is the flow velocity, ρ is the density, z is the flow directioncoordinate, λ is the friction coefficient, D_(H) is the equivalentdiameter of the throttle groove, and P is the pressure) is applied tothe throttle groove 4 of the present invention. u is defined as the meanflow velocity in the throttle groove cross section, ρ as the density,and z-axis as the fluid flow direction (it is referred to as the flowdirection coordinate z). Furthermore, the length of the main throttlegroove is given as L₀, the length of the entrance throttle groove isgiven as L_(E), and the position coordinate L of the flow rateregulating slider 10 (it is referred to as “lift”) is L=L₀ at thefinishing end position of said main throttle groove, and L=0 at thestarting end position. In addition, the flow rate regulating slider 10position is given by the dimensionless coordinate ζ*=1−L* that isstandardized by L₀, with the dimensionless lift L*=L/L₀ in which L isstandardized by L₀, and the starting end position of the main throttlegroove as the origin.

FIG. 6 is a schematic diagram of the throttle groove 4 of the presentinvention. The momentum equation (1) of the fluid in the tube passageshown in FIG. 6 is applied to the fluid in the throttle groove of thepresent invention. As described above, the equivalent diameter in theequation is defined by D_(H)=4A/U, by using the cross section area A ofthe flow passage, and its circumference U. It is the representativelength that indicates the equivalence of the flow passage in question toa cylindrical pipe whose diameter is to be calculated. For example, whenthe cross-section form is a semicircle of diameter D, throughA=(½)π(D/2)² and U=D+π(D/2), the equivalent diameter D_(H) becomes

D _(H)={(2π)^(0.5)/(1+π/2)}·A ^(0.5)   (15).

Even for a cross section form aside from semicircular, if it is across-section form that is similar and does not comprise a complicatedsurface that entwine inward, because there exists a relation thatcircumference U is proportional to A^(0.5), it is established thatD_(H)∝A^(0.5) which is found in the equation (15).

Subsequently, from the momentum equation (1), the basic relationalequation between the desired valve characteristic and the criticallength of the entrance throttle groove is derived.

FIG. 7 is a process chart for the calculation of the momentum equationof the present invention. Said momentum equation (1) is duplicated asthe equation (1-1). The flow velocity u is related with the mass flowrate G by the following equation from the continuity condition offluids.

u=G/(ρA)   (2)

The friction coefficient λ for a laminar flow is expressed by thefollowing equation.

λ=64 μA/(uD _(H))   (5)

When the equations (2) and (5) are substituted into said momentumequation (1-1) and rearranged, the equation (1-2) is obtained.

Next, said momentum equation (1-2) is applied to the flow inside theentrance throttle groove at the time in which the valve is fully opened.By multiplying both sides by ρ, assuming that the maximum flow rate isG_(M), and the cross section area of the entrance throttle groove A_(E)is constant, the equation (1-3) is obtained when said momentum equation(1-2) is integrated along the entire length of the entrance throttlegroove. 1 and 2 denoted on the integral symbol of the equation (1-3)indicate the states of the inflow portion and the outflow portion. Inaddition, the upper integration limit F(L_(E)) of the first termindicates the value of the parameter {1/(ρA)} at the exit surface of theentrance throttle groove.

Next, when said lift L takes an arbitrary value (L=L), the equation(1-4) is obtained when the equation (1-2) is multiplied with ρ andintegrated from the inflow portion to the outflow portion, assuming thatthe flow rate that corresponds to lift L from the given valvecharacteristic is G. The integration of the second term of the left handside of this equation (1-4) is done throughout the entire entrancethrottle groove, and from the entrance of the main throttle groove up tothe lift L. In other words, the extent of z is from 0 to {L_(E)+(L₀−L)},and may be divided into the entrance domain from 0 to L_(E), and themain domain from L_(E) to (L₀−L). In order to perform the integration onthis main domain, the dimensionless coordinate ζ and said dimensionlesscoordinate ζ* (=1−L*), with the origin at the starting end position ofthe main throttle groove, are used. The dimensionless coordinate ζ isdefined by

ζ=(z−L _(E))/L ₀   (16)

and when dz is variable-transformed to dζ,

dz=L₀dζ  (17)

is obtained.

The second term of the equation (1-4) may be divided into two parts,said main domain (variable ζ: 0-1) and entrance domain (variable z:0-L_(E)), and the equation (1-5) is obtained. When this equation (1-5)is substituted into the equation (1-4), the equation (1-6) is obtained.In addition, because A in the first term of the left hand side of theequation (1-4) is a function of ζ, the upper limit value of the integralcan be written as F(ζ*). In other words, it signifies that concerningthe parameter {(1/ρA)}, the integral is performed from the inflowportion 1 to ζ*. Because the third term of the equation (1-3) and thefourth term of the equation (1-6) are equal, the equation (1-7) isobtained when these are substituted. When this equation (1-7) is dividedby G, then substituted with G*=G/G_(M), it becomes the equation (1-8).

FIG. 8 is a process chart for the derivation of the relational equationof the present invention. When the equation (1-8) is differentiated withrespect to ζ*, it becomes the equation (2-1). Because the dimensionlesscoordinate ζ* is (=1−L*), when ζ* is rewritten by L*, the equation (2-3)is obtained. L_(E) satisfying the condition equation (2-3) in which theleft hand side of this equation (2-2) becomes 0 is defined as thecritical length L_(EC). This critical length L_(EC) has an implicationthat it is the optimum length of the entrance throttle groove that issuitable for the realization of the desired valve characteristic. Inother words, said condition equation (2-3) is used as the relationalequation for deriving the critical length L_(EC), which is the optimumlength of the entrance throttle groove, from the desired valvecharacteristic and the form of the main throttle groove. Therefore, fromsaid equation (2-3), said critical length L_(EC) is expressed byrelational equation (2-4). Because the physical property value is notincluded in this relational equation (2-4), it does not limit whetherthe fluid is liquid or gas. Said relational equation (2-4) is applied tovarious fluids. Furthermore, when the left hand side of the equation(2-2) is 0, the right hand side is also 0, and therefore the equation(2-5) is obtained.

FIG. 9 is a process chart for the derivation of the relational equationfor an incompressible fluid. The equation (3-1) shows the equation (2-5)shown in FIG. 8. When the fluid is a liquid that is incompressible, theintegral in the first term of the equation (3-1) becomes the equation(3-2), assuming that the cross section area of the inflow portion (1) issufficiently larger compared to the cross section area of the throttlegroove. On the other hand, the second term of the equation (3-1) can berewritten as the equation (3-3). By substituting the equation (3-2) andthe equation (3-3) into the equation (3-1), the equation (3-4) isobtained. Here, when it is rewritten using the dimensionless crosssection area A*=A/A_(E), it is expressed as the equation (3-5).Therefore, because the differential value of [(G*/A²)−(1/G*)] withrespect to L* is 0, as it is indicated in the equation (3-6), theequation (3-5) indicates that [(G*/A*²)−(1/G*)] is the constant C.Furthermore, at the time in which the valve is fully open, it becomesG*=1, A*²=1, and so constant C becomes 0. Therefore, said equation (3-6)at the time in which the valve is fully open becomes the equation (3-7),and therefore the relational equation (3-8) for an incompressible fluidis obtained.

FIG. 10 is a schematic diagram of the throttle groove 4 that havesimilar cross section forms. As described above, when the cross sectionsof the throttle groove 4 are similar, the equivalent diameter D_(H) ofthe throttle groove 4 is proportional to the power of 0.5 of the crosssection area A, and it becomes D_(H)∝A^(0.5). Even when the crosssection forms are trapezoidal as shown in the figure, only itscoefficient varies, and the relation of D_(H)∝A^(0.5) holds.

Therefore, as indicated by the equation (3-9) in FIG. 9, (A_(E)D_(HE)²)/(AD_(H) ²) at the right hand side of the equation (2-4) becomes1/A*². When the equation (3-9) is substituted into the equation (2-4),the relational equation (3-10) that yields the critical length forsimilar cross section forms is obtained. Furthermore, in the case wherethe fluid is incompressible, the relational equation (3-8) for saidincompressible fluid is realized for the relational equation (3-10), andtherefore the relational equation (3-11) for incompressible fluids andsimilar cross section forms is obtained.

FIG. 11 is a classification figure of the critical length in the casewhere the valve characteristic is of the linear type. G* and (dG*/L*)are included in said relational equation (2-4), and the relation betweenG* and L* is determined by the desired valve characteristic. As therepresentative valve characteristics, there are the linear type and theequal percentage type. Of these two types of valve characteristic, thecase of the linear type is explained first.

In the case in which the valve characteristic is of the linear type, thedimensionless flow rate G* is given by

G*=G ₀*+(1−G ₀*)·L*   (4-1)

Here, G₀* is the value of G* when L*=0, and the following relation holdswith the rangeability R_(A).

G ₀*=1/R _(A)   (4-2)

In the case where the finishing end of said main throttle groove has anideal form, the flow rate at the vicinity of the full opening stateconverges continuously toward 0. However, it is impossible to constructsuch finishing end form in reality. When the valve characteristic isexpressed by an equation, the initial flow rate G*₀ or the rangeabilityR_(A) is introduced. The valve characteristic of said linear type isexpressed as

G*=1/R _(A)+(1−1/R _(A))·L*   (4-3)

by using the rangeability R_(A). When (dG*/dL*) of the equation (4-3) issolved for, it becomes

(dG*/dL*)=(1−1/R _(A))   (4-4).

When the equations (4-3) and (4-4) are substituted into the relationalequation (2-4), the general relational equation (4-5) is derived for thecritical length for the valve characteristic of the linear type thatdoes not limit the type of the fluid and the form of the throttlegroove.

In the case where said main throttle valve has similar cross sectionforms, when the equations (3-9), (4-3), and (4-4) are substituted intosaid relational equation (2-4), the relational equation (4-6) isobtained for the critical length for similar cross section forms for thevalve characteristic of the linear type. Furthermore, when it is limitedto incompressible fluids/similar cross section forms, by substitutingthe equation (4-4) to the relational equation (3-11) of said criticallength, the relational equation (4-7) is derived for incompressiblefluids/similar cross section forms for the valve characteristic of thelinear type. In addition, in the case for incompressible fluids/similarcross sections, for an entrance throttle groove that has the criticallength L_(EC), the cross section area of the main throttle groove hasthe relation such that

A*=1/R _(A)+(1−1/R _(A))·L*   (4-8)

Furthermore, when the rangeability is infinitely large, from saidrelational equation (4-7), the critical length L_(EC) becomes

L_(EC)=L₀   (4-9)

Therefore, to impart the valve characteristic of the linear type to aminute flow rate controller that manipulate an incompressible fluid, itis suitable that the cross section forms of the main entrance groove bemade similar, and its length L₀ and the critical length L_(EC) of theentrance throttle groove be made equal.

FIG. 12 is a correlation diagram of the cross section area A and theflow rate Q of the main throttle groove in the minute flow ratecontroller, to which the valve characteristic of the linear type isimparted. The fluid is water whose viscosity is 1.01×10⁻³ Pa·s, thedifferential pressure between the inflow port and the outflow port ismade to be 0.1 MPa, the length L₀ of the main throttle groove is made tobe 10 mm, the cross section forms are similar semicircles, and therangeability is set to be infinitely large. That is to say, in the casewhere the condition for incompressible fluid/similar cross sections isfulfilled, it is designed so that by sliding said flow rate regulatingslider from the full closing state of the flow outflow port (L*=0) tothe full opening state (L*=1), said flow rate Q changes linearly from 0to the maximum flow rate.

In order to accomplish the previously stated design objective, as thecritical length L_(EC) of the entrance throttle groove, it is calculatedby using the equation (4-7) for the case for incompressiblefluid/similar cross section forms. However, in this case, because therangeability is made to be infinitely large, said critical length L_(EC)is made to be of equal length to L₀ from the equation (4-7). In otherwords, it is set to 10 mm. As it is clear from the figure, by forming anentrance throttle groove that has said critical length, the valvecharacteristic of the linear type of high precision can be imparted uponthe minute flow rate controller just by linearly increasing the crosssection A (□) of said main throttle groove.

On the other hand, in the case of absence of an entrance throttle groove(L_(E)=0) which is indicated by the bold line, said cross section area A(bold line) increases monotonically along with the increase of said liftL* up to the vicinity of L*=0.5. However, in order to realize said valvecharacteristic of the linear type, it is necessary that said crosssection area A is decreased and reduced as the full opening state (L*=1)is approached, and it has the maximum value of the cross section area atthe vicinity of the dimensionless lift L*=0.7. Therefore, in a minuteflow rate controller without an entrance throttle groove, there is theenlarged portion in the main throttle groove. In order to form on thevalve member a minuscule main throttle groove that has such enlargedportion, an extremely high processing technique is required, and at thesame time, it is extremely difficult to form a throttle groove that cansupply the flow rate with stability and high precision.

FIG. 13 is a correlation diagram of the cross section area A and theflow rate Q of the main throttle groove in a minute flow rate controllerto which the valve characteristic of the linear type is imparted. Thefluid is the case where the viscosity is about 30 times greater than thepreviously discussed water (for example, transformer oil of 3.16×10⁻²Pa·s), and the other conditions are set to the same values as in thecase where water in FIG. 12 was used. In other words, the differentialpressure between said input flow and output flow is 0.1 MPa, the lengthL₀ of the main throttle groove is 10 mm, the cross sections have similarsemicircular forms, and the rangeability is set to be infinitely large.The flow rate Q that flows out of said minute flow rate controller alsoincreases linearly as the dimensionless lift L* changes from 0 to 1, andsaid main throttle groove has the valve characteristic of the lineartype.

Here, the length L_(E) of the entrance throttle groove is set to be thecritical length L_(EC), and the rangeability is set to be infinitelylarge under the condition of incompressible fluid/similar cross sectionforms, and therefore, by the equation (4-7), said critical length L_(EC)is set to 10 mm, the equal length as L₀. As it is clear from the figure,even in the case where transformer oil is used, whose viscosity isgreater than that of water by an order or more of magnitude, by formingan entrance throttle groove with said critical length, a valvecharacteristic of the linear type of high precision is imparted upon theminute flow rate controller, through the throttle groove that has asimple structure.

On the other hand, in the case of absence of an entrance throttle grooveas indicated by the bold line, said cross section area A (bold line)increases monotonically with the increase of said lift L up to thevicinity of L*=0.9. However, as the fully opening state (L*=1) isapproached, the cross section of the main throttle groove suddenlydecreases. Such sudden change of the cross section of the main throttlegroove is caused by the fact that the viscosity of the transformer oilis greater (cf. FIG. 23, see below), compared to the case of waterindicated in FIG. 12. Therefore, the minute flow rate controller of thepresent invention, by being equipped with an entrance throttle grooveset at said critical length, does not change suddenly the cross sectionarea of the main throttle groove, and can impart the desired valvecharacteristic even in the case where it controls the flow rate of afluid with high viscosity.

FIG. 14 is a schematic diagram of a throttle groove having non-similarcross sections. The throttle groove 4 comprises cross sections ofrectangular form. Its height is constant, and width W of the throttlegroove decreases along the flow direction. That is to say, the crosssection of the fluid outflow port 20 changes to a non-similar form asthe flow rate regulating slider slides. Therefore, in order to determinethe critical length, it must be derived from relational equation (4-5)shown in FIG. 13. However, in said relational equation (4-5), L_(EC) isa function of the cross section area A, the equivalent diameter D_(H),and the dimensionless lift L*. This means even if L_(EC) is changed withthe degree of opening of the valve, or if the relation between the crosssection A, the equivalent diameter D_(H), and the dimensionless lift L*is determined such that L_(EC) becomes a constant, an indefinitenessremains for the value of L_(EC), and it is impossible to determine thevalue of L_(EC) uniquely.

As indicated in FIG. 13, the significance of equipping an entrancethrottle groove set to said critical length L_(EC) is that when thecross section area of the throttle groove increases suddenly in thevicinity of L*=1, this can be avoided. Therefore, in the case where saidthe cross sections of said main throttle groove is non-similar, whenL*=1 is set, and the other parameters are assumed to take the values atL*=1, the length obtained from said relational equation (4-5) is calledthe quasicritical length L_(EC), and the length of the entrance throttlegroove is determined by the quasicritical length L_(EC)=L₀/(1−1/R_(A)).

FIG. 15 is a correlation diagram of the cross section area A and theflow rate Q for a minute flow rate controller in which the length of theentrance throttle groove of the present invention is set to thequasicritical length L_(EC). The fluid is transformer oil whoseviscosity is 3.16×10⁻² Pa·s, the differential pressure between theinflow port and the outflow port is 0.1 MPa, the length L₀ of the mainthrottle groove is 10 mm, the quasicritical length L_(EC)=10.5 mm, themaximum flow rate Q_(M)=456 ml/m, the cross section forms arenon-similar rectangles as shown in FIG. 14, and the rangeability R_(A)is 20. Furthermore, as for the main throttle groove, the valvecharacteristic is set for the purpose of flow rate Q becoming of thelinear type (solid line within figure).

In the case that the length of said entrance throttle groove is set tothe quasicritical length L_(EC) (Δ), the cross section area A increasesmonotonically with the lift L*. Therefore, by setting the length of theentrance groove to said quasicritical length, an appropriate flowresistance is applied to the fluid, and the need for suddenly increasingthe throttle groove is avoided. On the other hand, in the case ofabsence of an entrance throttle groove (L_(E)=0) (□), the cross sectionarea A of the main throttle groove increases monotonically with theincrease of said lift L* up to the vicinity of L*=0.5; however, thecross section of the main throttle groove decreases as the fully openingstate (L*=1) is approached. Therefore, using the quasicritical length atthe fully opening state (L*=1) is effective for determining the lengthof said entrance throttle groove, when said main throttle groove isnon-similar.

FIG. 16 is a classification figure of the critical length when the valvecharacteristic is of the equal percentage (EQ) type. Next, as thedesired valve characteristic, the case of the equal percentage type isexplained in detail. In the case where the valve characteristic is ofthe equal percentage type, the dimensionless flow rate G* is given by

G=G ₀*^(1−L)*=(1/R _(A))^(1−L)*   (4-10)

and when (dG*/dL*) is derived from this equation (4-10), it becomes

(dG*/dL*)=−G*·ln G ₀ *=G*ln(R _(A))   (4-11)

When this equation (4-11) is substituted into the equation (2-4), thegeneral relational equation (4-12) that does no limit the type of thefluid and the form of the throttle groove is derived for critical lengthfor the equal percentage type valve characteristic shown in FIG. 16. Bythe same method as in the linear type, the relational equations (4-13)and (4-14) of FIG. 16 are obtained.

When the valve characteristic is of the equal percentage type, as forL_(EC), the critical length L_(EC) has become a function of L* in allcases for the general cross section form, incompressible fluid, and/orsimilar forms. Therefore, even for the equal percentage type valvecharacteristic, L_(EC) at the time of full opening (L*=1) is used as thequasicritical length. The quasicritical length L_(EC) in the case of theequal percentage type becomes

L _(EC) =L ₀/ln(R _(A))   (4-15)

Adopting said quasicritical length of the entrance throttle groove isreasonable and effective, regardless of the similarity or non-similarityof the cross section forms, or regardless of the presence or absence ofthe noncompressibility/compressibility of the fluid.

FIG. 17 is a correlation diagram of the cross section area A and theflow rate Q of the main throttle groove in a minute flow rate controllerto which the valve characteristic of the equal percentage type isimparted. The fluid is transformer oil whose viscosity is 3.16×10⁻²Pa·s, the differential pressure between the inflow port and the outflowport is 0.1 MPa, the critical length of the entrance throttle groove issuch that L_(EC)=3.34 mm, and the length L₀ of the main throttle grooveis set at 10 mm. Furthermore, a cross-section comprises semicircles thatare similar, and the rangeability R_(A) is set to 20.

From the valve characteristic of equal percentage type, as for the flowrate Q, the proportion of increment is becoming gradually larger in anexponential manner with the increase of the dimensionless lift L*, asindicated by the equation (4-10). The length of the entrance throttlegroove is determined from the relational equation (4-15) for thequasicritical length in the equal percentage type valve characteristic.When this entrance throttle groove is formed, the cross section area Aof said main throttle groove (□) increases monotonically, and the valvecharacteristic of the equal percentage type is imparted upon the minuteflow rate controller by the throttle groove with a simple structure.

On the other hand, in the case of absence of an entrance throttle groove(L_(E)=0) as indicated with the bold line, said cross section area A(bold line) monotonically increases with the increase in said lift L*,up to the vicinity of L*=0.9. However, the cross section area A takes onthe maximum value in the vicinity of L*=0.95, and the cross section areasuddenly decreases. That is to say, the cross section area of the mainthrottle groove must be increased suddenly from the starting endposition. To form such suddenly increasing portion on a throttle groove,it is regarded that a very high processing technique is required.

FIG. 18 is a correlation diagram between the dimensionless cross sectionarea A* and the dimensionless flow rate Q* of the main throttle groovein a minute flow rate controller to which the valve characteristic ofthe equal percentage type is imparted. This figure indicates thecorrelation between the dimensionless cross section area A* anddimensionless flow rate Q* for different lengths of the entrancethrottle groove: the case in which the length of said entrance throttlegroove is the quasicritical length L_(EC) that is determined by theequation (4-15) (⋄: L_(EC)=3.34 mm), the case in which this length isshorter than the quasicritical length L_(EC) (◯: L_(E)=2.23 mm), and thecase in which this length is longer than the quasicritical length L_(EC)(∘: L_(E)=5.01 mm). That is to say, it probes what kind of differencesoccurs between entrance throttle grooves whose lengths are thequasicritical length, 1/1.5 of this, and 1.5 times this. The fluid istransformer oil whose viscosity is 0.0316 Pa·s, the differentialpressure between the inflow port and the outflow port is 0.1 MPa, thelength L₀ of the main throttle groove is 10 mm, and the rangeabilityR_(A) is 20. As it is clear from the figure, even when said entrancethrottle groove is formed, the dimensionless cross section area A* doesnot become a monotonical change when its length differs from thecritical length determined from the equation (4-15). When it is shorterthan the critical length, it is necessary to increase the cross sectionarea A* of the main throttle groove suddenly; when it is longer than thecritical length, said cross section area A* must be decreased suddenly.

FIG. 19 is a schematic diagram of the throttle groove 4 having theshortened entrance throttle groove 8. For said entrance throttle groove,the flow resistance by this entrance throttle groove 8 is increased, andthe length of said entrance throttle groove 8 is shortened, by formingsaid entrance throttle groove in a tapered manner so that the crosssection area A_(EQ) of the starting end cross section 16 is smaller thanthe cross section area A_(E) of the finishing end cross section 19. Thelength of this shortened entrance throttle groove is defined as L_(EQ).

As for the method for determining the cross section area A_(EQ) andlength L_(EQ) necessary to generate, at said entrance throttle groove 8,the frictional pressure drop ΔP_(EF) which is equivalent to an entrancethrottle groove of the length L_(EC) having the uniform cross sectionarea A_(E), it is subsequently explained by taking as an example thecase in which the cross section forms are semicircular forms.

FIG. 20 is a process chart for deriving the length of the shortenedentrance throttle groove of the present invention. The frictionalpressure drop dP at the minute section dz of an entrance throttle groovehaving the cross section area A assumes the form of the equation (5-1)of FIG. 20. Here, the flow velocity u, the friction coefficient λ, andthe equivalent diameter D_(H) being given, when the following relationalequations that have been previously described,

u=G/(ρA)   (2)

λ=64 μA/(uD _(H))   (5)

D _(H)={(2π)^(0.5)/(1+π/2)}·A ^(0.5)   (15)

are substituted into the equation (5-1), the equation (5-2) is obtained.When this equation (5-2) is integrated along the entire length of theentrance throttle groove, the equation (5-3) describing the frictionalpressure drop ΔP_(EQ) in the entrance throttle groove is obtained. Here,when it is assumed that the cross section area A varies linearly towardthe flow direction coordinate z, then said cross section area A is givenby the equation (5-4). When its differentiated equation, the equation(5-5), is used for transforming the variable of the equation (5-3), andthen integration is carried out, the final frictional pressure dropequation (5-6) is obtained. Similarly, the equation (5-7) that gives thefrictional pressure drop ΔP_(E) when the cross section area of theentrance throttle groove is uniform is obtained. By equalizing thispressure drop ΔP_(E) and the previously determined ΔP_(EQ), the equation(5-8) that gives the length of the shortened entrance throttle groovefrom the equations (5-6) and (5-7) is obtained. As this equation (5-8)makes clear, by decreasing the cross section area of the entrancethrottle groove toward the starting end cross section, the length of theentrance throttle groove can be shortened by a factor of (A_(EQ)/A_(E)),compared to the case in which the cross section area A_(E) is constant.

The present invention is not limited to the embodiments described above.Various modifications, design alterations, and others that do notinvolve a departure from the technical concept of the present inventionare also included in the technical scope of the present invention.

INDUSTRIAL APPLICABILITY

According to the method for designing a minute flow rate controller ofthe present invention, a minute flow rate controller of high precisionrequired upon developing microchemical processing technology which isattracting attention in recent years in synthetic chemistry, analyticalchemistry, semiconductor industry and biotechnology industry, for usesfor immunoassay system, environmental analysis system, cell biochemistryexperimental system, chemical vapor growth system and syntheticchemistry experimental system, can be designed. Furthermore, through theincrease in reaction yield, the shortening of reaction time, and thereduction of burden to the environment, the control of chemicalreactions can be made highly precise and efficient. In addition,microminiaturization and integration of chemical reaction systems thatrequire minute and precise flow rate control, which is impossible withthe existing technology, can be realized.

1. A method of designing a minute flow rate controller equipped with anentrance throttle groove, said minute flow rate controller comprising aninflow passage for introducing a fluid, a valve member on which a mainthrottle groove is formed, for flowing the fluid introduced from saidinflow passage from a starting end to a finishing end, a flow rateregulating component that hermetically seals said main throttle grooveup to a desired position, a fluid outflow port that opens by said flowrate regulating component at a given cross section of said main throttlegroove, and an outflow passage that lead out the fluid that flows out ofsaid fluid outflow port, wherein an entrance throttle groove thatprecedes connectively is established at the starting end cross sectionof said main throttle groove, and the dimension of the entrance throttlegroove is determined so as to exhibit a desired flow resistance, basedon a relational equation derived from a momentum equation of the fluidthat flows through said entrance throttle groove and main throttlegroove.
 2. The method for designing a minute flow rate controllerequipped with an entrance throttle groove according to claim 1, whereinthe dimension of said entrance throttle groove is determined so thatwhen the cross section area of said main throttle groove monotonicallydecreases from the starting end to the finishing end, the flow rate ofthe fluid that flows out from said fluid outflow port monotonicallydecreases, as the position of said fluid outflow port moves from thestarting end to the finishing end.
 3. The method for designing a minuteflow rate controller equipped with an entrance throttle groove accordingto claim 1, wherein the momentum equation of said fluid is expressed asuρ(du/dz)+(λ/D _(H))(½)u ² ρ+dP/dz=0 (here, u is the flow velocity, ρ isthe density, z is the flow direction coordinate of fluid, λ is thefriction coefficient, D_(H) is the equivalent diameter of throttlegroove cross section area, and P is the pressure).
 4. The method fordesigning a minute flow rate controller equipped with an entrancethrottle groove according to claim 3, wherein said momentum equation iscomputed based uponu=G/(ρA) and λ=64 μA/(GD _(H)) (here, G is the mass flow rate, ρ is thefluid density, A is the cross section area of the fluid outflow port,and μ is the viscosity coefficient of the fluid).
 5. The method fordesigning a minute flow rate controller equipped with an entrancethrottle groove according to claim 4, wherein the critical length of theentrance throttle groove L_(EC) is given asL _(EC) =L ₀/(dG*/dL*)_(L)*₌₁ whenever the finishing end position ofsaid main throttle groove is set at L=0, the position of the fluidoutflow port is set at L=L, the starting end position is set at L=L₀,the flow rate when the fluid outflow port is located at L=L₀ is set atG_(M), the flow rate when the fluid output port is located at L=L is setat G, and the value of (dG*/dL*) at L*=L/L₀, G*=G/G_(M), and the valueof (dG*/dL*) at L*=1 is set to (dG*/dL*)_(L)*₌₁.
 6. The method fordesigning a minute flow rate controller equipped with an entrancethrottle groove according to claim 5, wherein the critical length L_(EC)corresponding to the linear type, in which the valve characteristic maybe expressed as G*=L*, is given asL_(EC)=L₀ whenever said fluid is an incompressible fluid, and the formsof given cross sections of the main throttle groove are similar figures.7. The method for designing a minute flow rate controller equipped withan entrance throttle groove according to claim 4, wherein said criticallength L_(EC) is given byL _(EC) =L ₀/(dG*/dL*) whenever the finishing end position of said mainthrottle groove is at L=0, the position of the fluid outflow port is atL=L, the starting end position is at L=L₀, the flow rate when the fluidoutflow port is at L=L₀ is G_(M), the flow rate when the fluid outflowis at L=L is G, the forms of given cross sections of said main throttlegroove are non-similar figures, and the valve characteristic is of thelinear type.
 8. The method for designing a minute flow rate controllerequipped with an entrance throttle groove according to claim 5 or 7,wherein said critical length L_(EC) is given byL _(EC) =L ₀/(1−1/R _(A)) whenever the valve characteristic is of thelinear type, and may be expressed asG*=G ₀*+(1−G ₀*)L* (here, G₀* is the value of G* at L*=0), and may beexpressed as G₀*=1/R_(A)(1≦R_(A)≦∞).
 9. The method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to claim 5 or 7, wherein said critical length L_(EC) is givenasL _(EC) =L ₀/ln(R _(A)) whenever the valve characteristic is of theequal percentage type that may be expressed asG*=G ₀*^((1−L)*⁾ (here, G₀* is the value of G* when L*=0), and whereG₀*=1/R_(A)(1≦R_(A)≦∞).
 10. The method for designing a minute flow ratecontroller equipped with an entrance throttle groove according to claim1, wherein it is equipped with an entrance throttle groove in which thecross section area of said entrance throttle groove increasesmonotonically toward the starting end position of said main throttlegroove.
 11. The method for designing a minute flow rate controllerequipped with an entrance throttle groove according to claim 10, whereinthe cross section area A_(E)(z) of said entrance throttle grooveincreases linearly along the flow direction coordinate z, and said crosssection area A_(E)(z) is given asA _(E)(z)=A _(EQ)+{(A _(E0) −A _(EQ))/L _(EQ) }·z (here, A_(EQ) is thestarting end cross section area of the entrance throttle groove, A_(E0)is the finishing end cross section area of the entrance throttle groovenearest to the starting end position of said main throttle groove,L_(EQ) is the length of the entrance throttle groove, and z is the flowdirection coordinate of the fluid).
 12. The method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to claim 11, wherein the finishing end position of said mainthrottle groove is L=0, the starting end position is L=L₀, the flow ratewhen the fluid overflow port is at L=0 is G₀, the flow rate when thefluid overflow port is at L=L₀ is G_(M), G₀*=G₀/G_(M), R_(A)=1/G₀*, andthe subsequent length $\begin{matrix}{L_{EQ} = {\left( {A_{EQ}/A_{E\; 0}} \right)\left\{ {L_{0}/\left( {1 - G_{0}^{*}} \right)} \right\}}} \\{= {\left( {A_{EQ}/A_{E\; 0}} \right)\left\{ {L_{0}/\left( {1\text{-}{1/R_{A}}} \right)} \right\}}}\end{matrix}$ of the entrance throttle groove, obtained by assuming thatthe frictional pressure drop inside said entrance throttle groove takesan equivalent quantity to the frictional pressure drop exhibited by anentrance throttle groove with a constant cross section area whosecritical length L_(EC), is taken.
 13. The method for designing a minuteflow rate controller equipped with an entrance throttle groove accordingclaim 2, wherein it is equipped with an entrance throttle groove inwhich the cross section area of said entrance throttle groove increasesmonotonically toward the starting end position of said main throttlegroove.
 14. The method for designing a minute flow rate controllerequipped with an entrance throttle groove according claim 3, wherein itis equipped with an entrance throttle groove in which the cross sectionarea of said entrance throttle groove increases monotonically toward thestarting end position of said main throttle groove.
 15. The method fordesigning a minute flow rate controller equipped with an entrancethrottle groove according claim 4, wherein it is equipped with anentrance throttle groove in which the cross section area of saidentrance throttle groove increases monotonically toward the starting endposition of said main throttle groove.
 16. The method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to any one of claims 13, 14 and 15, wherein the cross sectionarea A_(E)(z) of said entrance throttle groove increases linearly alongthe flow direction coordinate z, and said cross section area A_(E)(z) isgiven asA _(E)(z)=A _(EQ)+{(A _(E0) −A _(EQ))/L _(EQ) }·z (here, A_(EQ) is thestarting end cross section area of the entrance throttle groove, A_(E0)is the finishing end cross section area of the entrance throttle groovenearest to the starting end position of said main throttle groove,L_(EQ) is the length of the entrance throttle groove, and z is the flowdirection coordinate of the fluid).
 17. The method for designing aminute flow rate controller equipped with an entrance throttle grooveaccording to claim 16, wherein the finishing end position of said mainthrottle groove is L=0, the starting end position is L=L₀, the flow ratewhen the fluid overflow port is at L=0 is G₀, the flow rate when thefluid overflow port is at L=L₀ is G_(M), G₀*=G₀/G_(M), R_(A)=1/G₀*, andthe subsequent length $\begin{matrix}{L_{EQ} = {\left( {A_{EQ}/A_{E\; 0}} \right)\left\{ {L_{0}/\left( {1 - G_{0}^{*}} \right)} \right\}}} \\{= {\left( {A_{EQ}/A_{E\; 0}} \right)\left\{ {L_{0}/\left( {1\text{-}{1/R_{A}}} \right)} \right\}}}\end{matrix}$ of the entrance throttle groove, obtained by assuming thatthe frictional pressure drop inside said entrance throttle groove takesan equivalent quantity to the frictional pressure drop exhibited by anentrance throttle groove with a constant cross section area whosecritical length L_(EC), is taken.